THEORY OF SINGLE-PHASE MOTOR 231 



shows us that in this case the coil will tend to move to the left. 

 Thus a negative value of T, corresponds to a force acting from left 

 to right, or in the positive direction. 



From this it will be at once seen that any coil for which x < AT 

 experiences a pull in the positive direction (from left to right), while 

 any coil for which r > x > \T experiences a pull in the negative direc- 

 tion (from right to left). And since corresponding to every coil at a 

 distance x from the origin there is another at a distance x -f \T, it 

 follows that the tangential pulls acting on the various coils will 

 balance each other so that the resultant torque on the rotor of a single- 

 phase motor which is at rest vanishes. A single-phase induction motor 

 is, therefore, not self-starting. 



137. Torque Exerted by Single-phase Induction 

 Motor when Running 



Let us next investigate the relations which obtain when the motor 

 is running. Considering any one coil, we must now regard x as 

 variable, and we may write x = vt, v being the peripheral velocity of 

 the rotor. The positive direction of a; in Fig. 144 being from left to 

 right, this would correspond to a displacement of the coil from left 

 to right. The magnetic flux / at any time t is now given by ( 136) 



,. 2rl^ . irv. 



f = B sin pt cos t 



7T T 



r 



= r {sin (p + o>) -f sin (p - a))t} 



to standing for . The e.m.f. induced by this flux is 



ftf 7R 



e = - -i = - T {(p + to) cos (p + i)t + (p - to) cos (p - 



while the current is given by 



P "T" w _ r/._ \, / T 



0! and da being given by the equations- 

 tan 0i = ~ ^ ; tan 0. 2 = ^ ... (2) 



